Do not (ab)use git or any version control system for this.
Use NuGet.
You don't want to directly include other projects. Instead, pack every dependency into a .nuget package and use that for dependency handling. While submodules seems a solution to the problem, in practice, you are much better off using a proper dependency management instead of just including other projects.
TeamCity and other CI systems, evneeven TFS, allow you to automatically build new nuget packages, and TeamCity can also act as a nuget server.
And if you do not want to use a 'real' NuGet server, you can also just use a shared drive somewhere on your intranet.